This is story-based and can't be missed.
After the missions with Zorah Magdoros have concluded, the game switches over to High Rank missions and monsters. It's the same idea as before: Grind to get new gear, which lets you hunt new monsters, which lets you grind new gear.
You have to investigate a new kind of Anjanath to get it started, which gives you the "right" for six-star assignments. Once that's done, you start hunting a new kind of Rathian. Upon completing the quest Old Monster In The New World, you'll unlock this achievement.